Simplify (5m^-2)(2m^-3)

$(5 m^{- 2}) (2 m^{- 3})$

Step 1

Rewrite using the commutative property of multiplication.

$5 \cdot 2 m^{- 2} m^{- 3}$

Step 2

Multiply $m^{- 2}$ by $m^{- 3}$ by adding the exponents.

Move $m^{- 3}$ .

$5 \cdot 2 (m^{- 3} m^{- 2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 \cdot 2 m^{- 3 - 2}$

Subtract $2$ from $- 3$ .

$5 \cdot 2 m^{- 5}$

Step 3

Multiply $5$ by $2$ .

$10 m^{- 5}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$10 \frac{1}{m^{5}}$

Step 5

Combine $10$ and $\frac{1}{m^{5}}$ .

$\frac{10}{m^{5}}$